You may look cute wearing clothes in some fabrics, but you won't be warm. Cotton, everyone's usual favorite, is actually one of the worst to wear in the winter. Even though cotton is a natural fiber, it absorbs moisture and doesn't hold on to heat very well. In extreme conditions, this can leave you shivering and wet, and even with hypothermia in the worst cases (via Magnolia & Tulle). The Mayo Clinic even states on their website that cotton does a poor job of holding body heat and recommends wool, silk, or polypropylene as alternate inner layers. Since sometimes you'll be unable to ditch cotton altogether, we suggest layering an insulating skin-tone colored top underneath.
Synthetic fabrics like polyester, acrylic, and rayon should also be avoided in the winter. They are not breathable, will trap heat, and make you sweat. However, it is worth mentioning that there are new technologies, especially in activewear, where synthetic performance fabrics have some advantages. For example, fleece is made from polyester. Outerwear often utilizes polyester fleece designed to keep you well insulated and dry using effective sweat-wicking technology (via Magnolia & Tulle).